Laliga dataset
Le Cong Khanh 21110320
2024-05-31
Import The Dataset
pacman::p_load(
ggplot2,
mvtnorm,
GGally,
corrplot,
readxl,
tidyverse,
gridExtra,
grid,
plotly,
ggcorrplot,
FactoMineR,
factoextra
)data = read_excel("la_liga.xlsx")Data and Methods:
Information About The Dataset
Team: Name of the football team.
Points: Number of points earned in the season.
Matches: Total number of matches played in the season.
Wins: Number of matches won.
Draws: Number of matches drawn.
Loses: Number of matches lost.
Goals.scored: Number of goals scored.
Goals.conceded: Number of goals conceded.
Difference.goals: Goal difference (goals scored minus goals conceded).
Percentage.scored.goals: Average number of goals scored per match.
Percentage.conceded.goals: Average number of goals conceded per match.
Shots: Total number of shots.
Shots.on.goal: Number of shots on target.
Penalties.scored: Number of goals scored from penalties.
Assistances: Number of assists.
Fouls.made: Number of fouls committed.
Matches.without.conceding: Number of matches with a clean sheet (no goals conceded).
Yellow.cards: Number of yellow cards received.
Red.cards: Number of red cards received.
Offsides: Number of offsides.
Remark on the dataset:
The dataset contains 20 rows and 20 columns which no duplicate or missing values. All columns are positive number.
Methods:
To identify the indicators that influence football performance, we perform a comparative analysis between teams of varying success levels. Often, we encounter datasets with many related categories; hence, applying techniques to reduce the quantity of data can be beneficial. In this study, we aim to reduce the dimensions of a data matrix without losing relevant information by using Principal Component Analysis (PCA). Subsequently, we utilize these principal components to identify the performance differences between the top and bottom teams in LaLiga.
head(data)## # A tibble: 6 × 20
## Team Points Matches Wins Draws Loses Goals.scored Goals.conceded
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 Barcelona 91 38 29 4 5 112 29
## 2 Real Madrid 90 38 28 6 4 110 34
## 3 Atlético Madrid 88 38 28 4 6 63 18
## 4 Villarreal 64 38 18 10 10 44 35
## 5 Athletic 62 38 18 8 12 58 45
## 6 Celta 60 38 17 9 12 51 59
## # ℹ 12 more variables: Difference.goals <dbl>, Percentage.scored.goals <dbl>,
## # Percentage.conceded.goals <dbl>, Shots <dbl>, Shots.on.goal <dbl>,
## # Penalties.scored <dbl>, Assistances <dbl>, Fouls.made <dbl>,
## # Matches.without.conceding <dbl>, Yellow.cards <dbl>, Red.cards <dbl>,
## # Offsides <dbl>str(data)## tibble [20 × 20] (S3: tbl_df/tbl/data.frame)
## $ Team : chr [1:20] "Barcelona" "Real Madrid" "Atlético Madrid" "Villarreal" ...
## $ Points : num [1:20] 91 90 88 64 62 60 52 48 48 45 ...
## $ Matches : num [1:20] 38 38 38 38 38 38 38 38 38 38 ...
## $ Wins : num [1:20] 29 28 28 18 18 17 14 12 13 11 ...
## $ Draws : num [1:20] 4 6 4 10 8 9 10 12 9 12 ...
## $ Loses : num [1:20] 5 4 6 10 12 12 14 14 16 15 ...
## $ Goals.scored : num [1:20] 112 110 63 44 58 51 51 38 45 34 ...
## $ Goals.conceded : num [1:20] 29 34 18 35 45 59 50 35 48 52 ...
## $ Difference.goals : num [1:20] 83 76 45 9 13 -8 1 3 -3 -18 ...
## $ Percentage.scored.goals : num [1:20] 2.95 2.89 1.66 1.16 1.53 1.34 1.34 1 1.18 0.89 ...
## $ Percentage.conceded.goals: num [1:20] 0.76 0.89 0.47 0.92 1.18 1.55 1.32 0.92 1.26 1.37 ...
## $ Shots : num [1:20] 600 712 481 346 450 442 460 452 454 398 ...
## $ Shots.on.goal : num [1:20] 277 299 186 135 178 170 189 170 164 132 ...
## $ Penalties.scored : num [1:20] 11 6 1 3 3 4 6 2 1 3 ...
## $ Assistances : num [1:20] 79 90 49 32 42 43 35 27 33 26 ...
## $ Fouls.made : num [1:20] 385 420 503 534 502 528 555 552 465 490 ...
## $ Matches.without.conceding: num [1:20] 18 14 24 17 13 10 11 12 13 12 ...
## $ Yellow.cards : num [1:20] 66 72 91 100 84 116 106 110 108 110 ...
## $ Red.cards : num [1:20] 1 5 3 4 5 6 7 5 5 3 ...
## $ Offsides : num [1:20] 120 114 84 106 92 103 106 85 85 80 ...Exploratory Data Analysis
1. Data Overview
We will add some features to the original dataset to facilitate data exploration, simultaneously, deviding the teams into two group.
data <- data %>%
mutate(
Effectiveness.Percentage = round(((Goals.scored + Shots.on.goal) / Shots) * 100, digits=2),
Rank = row_number(),
Team.Level = case_when(
Rank <= 6 ~ "Top",
Rank > 6 & Rank < 14 ~ "Middle",
TRUE ~ "Bottom")
)
data = data[, -c(22)]
str(data)## tibble [20 × 22] (S3: tbl_df/tbl/data.frame)
## $ Team : chr [1:20] "Barcelona" "Real Madrid" "Atlético Madrid" "Villarreal" ...
## $ Points : num [1:20] 91 90 88 64 62 60 52 48 48 45 ...
## $ Matches : num [1:20] 38 38 38 38 38 38 38 38 38 38 ...
## $ Wins : num [1:20] 29 28 28 18 18 17 14 12 13 11 ...
## $ Draws : num [1:20] 4 6 4 10 8 9 10 12 9 12 ...
## $ Loses : num [1:20] 5 4 6 10 12 12 14 14 16 15 ...
## $ Goals.scored : num [1:20] 112 110 63 44 58 51 51 38 45 34 ...
## $ Goals.conceded : num [1:20] 29 34 18 35 45 59 50 35 48 52 ...
## $ Difference.goals : num [1:20] 83 76 45 9 13 -8 1 3 -3 -18 ...
## $ Percentage.scored.goals : num [1:20] 2.95 2.89 1.66 1.16 1.53 1.34 1.34 1 1.18 0.89 ...
## $ Percentage.conceded.goals: num [1:20] 0.76 0.89 0.47 0.92 1.18 1.55 1.32 0.92 1.26 1.37 ...
## $ Shots : num [1:20] 600 712 481 346 450 442 460 452 454 398 ...
## $ Shots.on.goal : num [1:20] 277 299 186 135 178 170 189 170 164 132 ...
## $ Penalties.scored : num [1:20] 11 6 1 3 3 4 6 2 1 3 ...
## $ Assistances : num [1:20] 79 90 49 32 42 43 35 27 33 26 ...
## $ Fouls.made : num [1:20] 385 420 503 534 502 528 555 552 465 490 ...
## $ Matches.without.conceding: num [1:20] 18 14 24 17 13 10 11 12 13 12 ...
## $ Yellow.cards : num [1:20] 66 72 91 100 84 116 106 110 108 110 ...
## $ Red.cards : num [1:20] 1 5 3 4 5 6 7 5 5 3 ...
## $ Offsides : num [1:20] 120 114 84 106 92 103 106 85 85 80 ...
## $ Effectiveness.Percentage : num [1:20] 64.8 57.4 51.8 51.7 52.4 ...
## $ Team.Level : chr [1:20] "Top" "Top" "Top" "Top" ...data## # A tibble: 20 × 22
## Team Points Matches Wins Draws Loses Goals.scored Goals.conceded
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 Barcelona 91 38 29 4 5 112 29
## 2 Real Madrid 90 38 28 6 4 110 34
## 3 Atlético Madrid 88 38 28 4 6 63 18
## 4 Villarreal 64 38 18 10 10 44 35
## 5 Athletic 62 38 18 8 12 58 45
## 6 Celta 60 38 17 9 12 51 59
## 7 Sevilla 52 38 14 10 14 51 50
## 8 Málaga 48 38 12 12 14 38 35
## 9 Real Sociedad 48 38 13 9 16 45 48
## 10 Betis 45 38 11 12 15 34 52
## 11 Las Palmas 44 38 12 8 18 45 53
## 12 Valencia 44 38 11 11 16 46 48
## 13 Eibar 43 38 11 10 17 49 61
## 14 Espanyol 43 38 12 7 19 40 74
## 15 Deportivo 42 38 8 18 12 45 61
## 16 Granada 39 38 10 9 19 46 69
## 17 Sporting Gijón 39 38 10 9 19 40 62
## 18 Rayo Vallecano 38 38 9 11 18 52 73
## 19 Getafe 36 38 9 9 20 37 67
## 20 Levante 32 38 8 8 22 37 70
## # ℹ 14 more variables: Difference.goals <dbl>, Percentage.scored.goals <dbl>,
## # Percentage.conceded.goals <dbl>, Shots <dbl>, Shots.on.goal <dbl>,
## # Penalties.scored <dbl>, Assistances <dbl>, Fouls.made <dbl>,
## # Matches.without.conceding <dbl>, Yellow.cards <dbl>, Red.cards <dbl>,
## # Offsides <dbl>, Effectiveness.Percentage <dbl>, Team.Level <chr>- Plot the distribution of numerical columns
plot_all_densities <- function(data, exclude_cols = c(1,3,22) , fill_color = "skyblue", alpha_value = 0.3, base_size = 15) {
plot_list <- list()
for (var in names(data[, -exclude_cols])) {
p = ggplot(data, aes_string(x = var)) +
geom_density(fill = "skyblue", color = "blue", alpha = alpha_value) +
theme_minimal(base_size = base_size) +
labs(title = var,
x = "",
y = "Density",
) +
geom_rug(sides = "b")
plot_list[[var]] <- p
}
title_grob <- textGrob("Distribution Of Numerical Columns", gp = gpar(fontsize = 20, fontface = "bold"))
grid.arrange(title_grob, grobs=plot_list, ncol = 5, nrow = 5)
}
plot_all_densities(data)## Warning: `aes_string()` was deprecated in ggplot2 3.0.0.
## ℹ Please use tidy evaluation idioms with `aes()`.
## ℹ See also `vignette("ggplot2-in-packages")` for more information.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.
plot_all_boxplot <- function(data, exclude_cols = c(1, 3, 22), fill_color = "skyblue", alpha_value = 0.3, base_size = 15) {
plot_list <- list()
for (var in names(data[, -exclude_cols])) {
p = ggplot(data, aes_string(x = var)) +
geom_boxplot(fill='palegreen3') +
theme_minimal(base_size = base_size) +
labs(title = var,
x = "",
y = "Value"
)
plot_list[[var]] <- p
}
grid.arrange(title_grob,
grobs=plot_list,
ncol = 5,
nrow = 5)
}
plot_all_boxplot(data)
These plots provide an overview of the distribution of football statistics in La Liga, showing a fairly even competition between teams, with some teams standing out. Points, wins, losses, and goals scored are all clustered around the median, with some teams like Barcelona, Real Madrid, or Atlético Madrid potentially having significantly higher metrics. Draws and fouls made are also tightly distributed, with a few teams tending to draw more or commit more fouls. Goal difference and win ratio percentage highlight a clear distinction between stronger and weaker teams, with some teams having notably high goal differences and win ratios. Goals conceded, offsides, yellow cards, and red cards also show a relatively tight distribution, reflecting the disciplined and strategic play of the teams. Metrics such as shots, shots on goal, and assists are evenly distributed, with some teams having notably more effective offenses. Overall, we illustrate the balance and intense competition in La Liga, with a few teams excelling in many key statistics.
2.Comparison between the team levels
top_teams <- data %>% filter(Team.Level == 'Top')
middle_teams <- data %>% filter(Team.Level == 'Middle')
bottom_teams <- data %>% filter(Team.Level == 'Bottom')
summary(top_teams)## Team Points Matches Wins Draws
## Length:6 Min. :60.00 Min. :38 Min. :17 Min. : 4.000
## Class :character 1st Qu.:62.50 1st Qu.:38 1st Qu.:18 1st Qu.: 4.500
## Mode :character Median :76.00 Median :38 Median :23 Median : 7.000
## Mean :75.83 Mean :38 Mean :23 Mean : 6.833
## 3rd Qu.:89.50 3rd Qu.:38 3rd Qu.:28 3rd Qu.: 8.750
## Max. :91.00 Max. :38 Max. :29 Max. :10.000
## Loses Goals.scored Goals.conceded Difference.goals
## Min. : 4.000 Min. : 44.00 Min. :18.00 Min. :-8.00
## 1st Qu.: 5.250 1st Qu.: 52.75 1st Qu.:30.25 1st Qu.:10.00
## Median : 8.000 Median : 60.50 Median :34.50 Median :29.00
## Mean : 8.167 Mean : 73.00 Mean :36.67 Mean :36.33
## 3rd Qu.:11.500 3rd Qu.: 98.25 3rd Qu.:42.50 3rd Qu.:68.25
## Max. :12.000 Max. :112.00 Max. :59.00 Max. :83.00
## Percentage.scored.goals Percentage.conceded.goals Shots
## Min. :1.160 Min. :0.4700 Min. :346.0
## 1st Qu.:1.387 1st Qu.:0.7925 1st Qu.:444.0
## Median :1.595 Median :0.9050 Median :465.5
## Mean :1.922 Mean :0.9617 Mean :505.2
## 3rd Qu.:2.583 3rd Qu.:1.1150 3rd Qu.:570.2
## Max. :2.950 Max. :1.5500 Max. :712.0
## Shots.on.goal Penalties.scored Assistances Fouls.made
## Min. :135.0 Min. : 1.000 Min. :32.00 Min. :385.0
## 1st Qu.:172.0 1st Qu.: 3.000 1st Qu.:42.25 1st Qu.:440.5
## Median :182.0 Median : 3.500 Median :46.00 Median :502.5
## Mean :207.5 Mean : 4.667 Mean :55.83 Mean :478.7
## 3rd Qu.:254.2 3rd Qu.: 5.500 3rd Qu.:71.50 3rd Qu.:521.8
## Max. :299.0 Max. :11.000 Max. :90.00 Max. :534.0
## Matches.without.conceding Yellow.cards Red.cards Offsides
## Min. :10.00 Min. : 66.00 Min. :1.00 Min. : 84.00
## 1st Qu.:13.25 1st Qu.: 75.00 1st Qu.:3.25 1st Qu.: 94.75
## Median :15.50 Median : 87.50 Median :4.50 Median :104.50
## Mean :16.00 Mean : 88.17 Mean :4.00 Mean :103.17
## 3rd Qu.:17.75 3rd Qu.: 97.75 3rd Qu.:5.00 3rd Qu.:112.00
## Max. :24.00 Max. :116.00 Max. :6.00 Max. :120.00
## Effectiveness.Percentage Team.Level
## Min. :50.00 Length:6
## 1st Qu.:51.74 Class :character
## Median :52.10 Mode :character
## Mean :54.70
## 3rd Qu.:56.19
## Max. :64.83cat('\n \n')summary(middle_teams)## Team Points Matches Wins Draws
## Length:7 Min. :43.00 Min. :38 Min. :11.0 Min. : 8.00
## Class :character 1st Qu.:44.00 1st Qu.:38 1st Qu.:11.0 1st Qu.: 9.50
## Mode :character Median :45.00 Median :38 Median :12.0 Median :10.00
## Mean :46.29 Mean :38 Mean :12.0 Mean :10.29
## 3rd Qu.:48.00 3rd Qu.:38 3rd Qu.:12.5 3rd Qu.:11.50
## Max. :52.00 Max. :38 Max. :14.0 Max. :12.00
## Loses Goals.scored Goals.conceded Difference.goals
## Min. :14.00 Min. :34.0 Min. :35.00 Min. :-18.000
## 1st Qu.:14.50 1st Qu.:41.5 1st Qu.:48.00 1st Qu.:-10.000
## Median :16.00 Median :45.0 Median :50.00 Median : -3.000
## Mean :15.71 Mean :44.0 Mean :49.57 Mean : -5.571
## 3rd Qu.:16.50 3rd Qu.:47.5 3rd Qu.:52.50 3rd Qu.: -0.500
## Max. :18.00 Max. :51.0 Max. :61.00 Max. : 3.000
## Percentage.scored.goals Percentage.conceded.goals Shots
## Min. :0.890 Min. :0.920 Min. :398.0
## 1st Qu.:1.090 1st Qu.:1.260 1st Qu.:409.5
## Median :1.180 Median :1.320 Median :421.0
## Mean :1.156 Mean :1.304 Mean :429.1
## 3rd Qu.:1.250 3rd Qu.:1.380 3rd Qu.:453.0
## Max. :1.340 Max. :1.610 Max. :460.0
## Shots.on.goal Penalties.scored Assistances Fouls.made
## Min. :132.0 Min. :1.000 Min. :26.00 Min. :465.0
## 1st Qu.:150.5 1st Qu.:2.500 1st Qu.:27.00 1st Qu.:477.5
## Median :164.0 Median :4.000 Median :33.00 Median :552.0
## Mean :160.7 Mean :3.714 Mean :30.57 Mean :527.4
## 3rd Qu.:169.5 3rd Qu.:5.000 3rd Qu.:33.00 3rd Qu.:561.0
## Max. :189.0 Max. :6.000 Max. :35.00 Max. :598.0
## Matches.without.conceding Yellow.cards Red.cards Offsides
## Min. : 7.00 Min. : 99.0 Min. :3 Min. : 79.00
## 1st Qu.: 9.00 1st Qu.:107.0 1st Qu.:4 1st Qu.: 82.50
## Median :11.00 Median :109.0 Median :5 Median : 85.00
## Mean :10.43 Mean :107.9 Mean :5 Mean : 87.43
## 3rd Qu.:12.00 3rd Qu.:110.0 3rd Qu.:6 3rd Qu.: 88.50
## Max. :13.00 Max. :113.0 Max. :7 Max. :106.00
## Effectiveness.Percentage Team.Level
## Min. :41.71 Length:7
## 1st Qu.:46.03 Class :character
## Median :47.13 Mode :character
## Mean :47.63
## 3rd Qu.:50.19
## Max. :52.17cat('\n \n')summary(bottom_teams)## Team Points Matches Wins
## Length:7 Min. :32.00 Min. :38 Min. : 8.000
## Class :character 1st Qu.:37.00 1st Qu.:38 1st Qu.: 8.500
## Mode :character Median :39.00 Median :38 Median : 9.000
## Mean :38.43 Mean :38 Mean : 9.429
## 3rd Qu.:40.50 3rd Qu.:38 3rd Qu.:10.000
## Max. :43.00 Max. :38 Max. :12.000
## Draws Loses Goals.scored Goals.conceded
## Min. : 7.00 Min. :12.00 Min. :37.00 Min. :61.0
## 1st Qu.: 8.50 1st Qu.:18.50 1st Qu.:38.50 1st Qu.:64.5
## Median : 9.00 Median :19.00 Median :40.00 Median :69.0
## Mean :10.14 Mean :18.43 Mean :42.43 Mean :68.0
## 3rd Qu.:10.00 3rd Qu.:19.50 3rd Qu.:45.50 3rd Qu.:71.5
## Max. :18.00 Max. :22.00 Max. :52.00 Max. :74.0
## Difference.goals Percentage.scored.goals Percentage.conceded.goals
## Min. :-34.00 Min. :0.970 Min. :1.610
## 1st Qu.:-31.50 1st Qu.:1.010 1st Qu.:1.695
## Median :-23.00 Median :1.050 Median :1.820
## Mean :-25.57 Mean :1.114 Mean :1.790
## 3rd Qu.:-21.50 3rd Qu.:1.195 3rd Qu.:1.880
## Max. :-16.00 Max. :1.370 Max. :1.950
## Shots Shots.on.goal Penalties.scored Assistances
## Min. :372.0 Min. :129.0 Min. :1.000 Min. :23.00
## 1st Qu.:409.0 1st Qu.:145.5 1st Qu.:1.000 1st Qu.:28.00
## Median :433.0 Median :155.0 Median :1.000 Median :31.00
## Mean :430.4 Mean :155.9 Mean :2.143 Mean :29.71
## 3rd Qu.:442.5 3rd Qu.:162.0 3rd Qu.:2.000 3rd Qu.:31.50
## Max. :505.0 Max. :192.0 Max. :7.000 Max. :35.00
## Fouls.made Matches.without.conceding Yellow.cards Red.cards
## Min. :401.0 Min. :4.000 Min. : 84.0 Min. :4.0
## 1st Qu.:527.5 1st Qu.:6.000 1st Qu.:111.0 1st Qu.:5.0
## Median :545.0 Median :7.000 Median :130.0 Median :6.0
## Mean :541.3 Mean :6.429 Mean :120.1 Mean :6.0
## 3rd Qu.:567.0 3rd Qu.:7.000 3rd Qu.:132.0 3rd Qu.:6.5
## Max. :654.0 Max. :8.000 Max. :141.0 Max. :9.0
## Offsides Effectiveness.Percentage Team.Level
## Min. : 72.00 Min. :42.56 Length:7
## 1st Qu.: 77.00 1st Qu.:44.52 Class :character
## Median : 85.00 Median :45.43 Mode :character
## Mean : 88.71 Mean :46.06
## 3rd Qu.: 93.50 3rd Qu.:47.55
## Max. :123.00 Max. :50.262.1. Attack and defense statistics
avg_assists_top <- round(mean(top_teams$Assistances), digits = 2)
avg_assists_middle <- round(mean(middle_teams$Assistances), digits = 2)
avg_assists_bottom <- round(mean(bottom_teams$Assistances), digits = 2)
avg_assists <- data.frame(
Team_Level = c("Top Teams", "Middle Teams", "Bottom Teams"),
Avg_Assists = c(avg_assists_top, avg_assists_middle, avg_assists_bottom)
)
ggplot(avg_assists, aes(x = Team_Level, y = Avg_Assists, fill = Team_Level)) +
geom_bar(stat = "identity", width = 0.5, color = "black") +
geom_text(aes(label = Avg_Assists), vjust = -0.5, color = "black", size = 4) +
labs(title = "Average Assists by Team Level",
x = "Team Level",
y = "Average Assists",
fill = "Team Level") +
theme_minimal() +
theme(legend.position = "none") +
scale_fill_manual(values = c("Top Teams" = "skyblue", "Middle Teams" = "lightgreen", "Bottom Teams" = "salmon"))
long_data <- data %>%
gather(key = "Metric", value = "Value", Shots, Shots.on.goal, Goals.scored)
avg_metrics <- long_data %>%
group_by(Team.Level, Metric) %>%
summarise(Average = mean(Value))## `summarise()` has grouped output by 'Team.Level'. You can override using the
## `.groups` argument.avg_metrics## # A tibble: 9 × 3
## # Groups: Team.Level [3]
## Team.Level Metric Average
## <chr> <chr> <dbl>
## 1 Bottom Goals.scored 42.4
## 2 Bottom Shots 430.
## 3 Bottom Shots.on.goal 156.
## 4 Middle Goals.scored 44
## 5 Middle Shots 429.
## 6 Middle Shots.on.goal 161.
## 7 Top Goals.scored 73
## 8 Top Shots 505.
## 9 Top Shots.on.goal 208.ggplot(avg_metrics, aes(x = Team.Level, y = Average, fill = Metric)) +
geom_bar(stat = "identity", position = position_dodge(), color = "black") +
geom_text(aes(label = round(Average, 2)), position = position_dodge(0.9), vjust = -0.5, size = 3) +
labs(title = "Comparison of Shots, Shots on Goal, and Goals Scored by Team Level",
x = "Team Level",
y = "Average Value",
fill = "Metric") +
theme_minimal() +
scale_fill_manual(values = c("Shots" = "skyblue", "Shots.on.goal" = "lightgreen", "Goals.scored" = "salmon"))
avg_top <- round(mean(top_teams$Effectiveness.Percentage), digits=2)
avg_bottom <- round(mean(bottom_teams$Effectiveness.Percentage), digits=2)
avg_middle <- round(mean(middle_teams$Effectiveness.Percentage), digits=2)
avg_effectiveness <- data.frame(
Team_Level = c("Top Teams", "Middle Teams" ,"Bottom Teams"),
Avg_effectiveness = c(avg_top, avg_middle, avg_bottom)
)
ggplot(avg_effectiveness, aes(x = Team_Level, y = Avg_effectiveness, fill = Team_Level)) +
geom_bar(stat = "identity", width = 0.5, color = "black") +
geom_text(aes(label = paste0(Avg_effectiveness, "%")), vjust = -0.5, color = "black", size = 4) +
labs(title = "Average Effectiveness Percentage by Team Level",
x = "Team Level",
y = "Average Effectiveness (%)",
fill = "Team Level") +
theme_minimal() +
theme(legend.position = "none") +
scale_fill_manual(values = c("Top Teams" = "skyblue", "Middle Teams" = "lightgreen", "Bottom Teams" = "salmon"))
2.2. Analysis of penalty cards.
avg_yellow_cards_top <- round(mean(top_teams$Yellow.cards / top_teams$Matches), digits = 2)
avg_yellow_cards_middle <- round(mean(middle_teams$Yellow.cards / middle_teams$Matches), digits = 2)
avg_yellow_cards_bottom <- round(mean(bottom_teams$Yellow.cards / bottom_teams$Matches), digits = 2)
avg_red_cards_top <- round(mean(top_teams$Red.cards / top_teams$Matches), digits = 2)
avg_red_cards_middle <- round(mean(middle_teams$Red.cards / middle_teams$Matches), digits = 2)
avg_red_cards_bottom <- round(mean(bottom_teams$Red.cards / bottom_teams$Matches), digits = 2)
avg_cards <- data.frame(
Team_Level = rep(c("Top Teams", "Middle Teams", "Bottom Teams"), each = 2),
Card_Type = rep(c("Yellow Cards", "Red Cards"), times = 3),
Avg_Cards = c(avg_yellow_cards_top, avg_red_cards_top,
avg_yellow_cards_middle, avg_red_cards_middle,
avg_yellow_cards_bottom, avg_red_cards_bottom)
)
ggplot(avg_cards, aes(x = Team_Level, y = Avg_Cards, fill = Card_Type)) +
geom_bar(stat = "identity", position = "dodge", width = 0.7, color = "black") +
geom_text(aes(label = Avg_Cards), position = position_dodge(width = 0.7), vjust = -0.5, size = 4) +
labs(title = "Average Yellow and Red Cards per Match by Team Level",
x = "Team Level",
y = "Average Cards per Match",
fill = "Card Type") +
theme_minimal() +
scale_fill_manual(values = c("Yellow Cards" = "yellow", "Red Cards" = "red"))
2.3. Analysis of tactical indicators:
total_fouls_top <- sum(top_teams$Fouls.made)
total_fouls_bottom <- sum(bottom_teams$Fouls.made)
total_fouls_middle <- sum(middle_teams$Fouls.made)
# Create a data frame for total fouls
total_fouls <- data.frame(
Team_Level = c("Top Teams", "Middle Teams" ,"Bottom Teams"),
Total_Fouls = c(total_fouls_top, total_fouls_middle ,total_fouls_bottom)
)
# Plot the bar chart
ggplot(total_fouls, aes(x = Team_Level, y = Total_Fouls, fill = Team_Level)) +
geom_bar(stat = "identity", width = 0.5, color = "black") +
geom_text(aes(label = Total_Fouls), vjust = -0.5, color = "black", size = 4) +
labs(title = "Total Fouls Committed by Team Level",
x = "Team Level",
y = "Total Fouls",
fill = "Team Level") +
theme_minimal() +
theme(legend.position = "none") +
scale_fill_manual(values = c("Top Teams" = "skyblue", "Middle Teams" = "lightgreen", "Bottom Teams" = "salmon"))
avg_offsides_top <- round(mean(top_teams$Offsides), digits = 2)
avg_offsides_middle <- round(mean(middle_teams$Offsides), digits = 2)
avg_offsides_bottom <- round(mean(bottom_teams$Offsides), digits = 2)
avg_offsides <- data.frame(
Team_Level = c("Top Teams", "Middle Teams", "Bottom Teams"),
Avg_Offsides = c(avg_offsides_top, avg_offsides_middle, avg_offsides_bottom)
)
ggplot(avg_offsides, aes(x = Team_Level, y = Avg_Offsides, fill = Team_Level)) +
geom_bar(stat = "identity", width = 0.5, color = "black") +
geom_text(aes(label = Avg_Offsides), vjust = -0.5, color = "black", size = 4) +
labs(title = "Average Offsides by Team Level",
x = "Team Level",
y = "Average Offsides",
fill = "Team Level") +
theme_minimal() +
theme(legend.position = "none") +
scale_fill_manual(values = c("Top Teams" = "skyblue", "Middle Teams" = "lightgreen", "Bottom Teams" = "salmon"))
corr_mat <- round(cor(data[, -c(1,3,22)]),2)
p_mat <- cor_pmat(data[, -c(1,3,22)])
# plotting the interactive corr heatmap
corr_mat <- ggcorrplot(
corr_mat, hc.order = TRUE, type = "lower",
outline.col = "white",
p.mat = p_mat
)
ggplotly(corr_mat)3. Principal Components Analysis
data.pca <- PCA(data[, -c(1,3,22)], graph=F)
data.pca## **Results for the Principal Component Analysis (PCA)**
## The analysis was performed on 20 individuals, described by 19 variables
## *The results are available in the following objects:
##
## name description
## 1 "$eig" "eigenvalues"
## 2 "$var" "results for the variables"
## 3 "$var$coord" "coord. for the variables"
## 4 "$var$cor" "correlations variables - dimensions"
## 5 "$var$cos2" "cos2 for the variables"
## 6 "$var$contrib" "contributions of the variables"
## 7 "$ind" "results for the individuals"
## 8 "$ind$coord" "coord. for the individuals"
## 9 "$ind$cos2" "cos2 for the individuals"
## 10 "$ind$contrib" "contributions of the individuals"
## 11 "$call" "summary statistics"
## 12 "$call$centre" "mean of the variables"
## 13 "$call$ecart.type" "standard error of the variables"
## 14 "$call$row.w" "weights for the individuals"
## 15 "$call$col.w" "weights for the variables"eig.val <- get_eigenvalue(data.pca)
eig.val## eigenvalue variance.percent cumulative.variance.percent
## Dim.1 1.257613e+01 6.619016e+01 66.19016
## Dim.2 2.440067e+00 1.284246e+01 79.03261
## Dim.3 1.310948e+00 6.899725e+00 85.93234
## Dim.4 8.385734e-01 4.413544e+00 90.34588
## Dim.5 7.582783e-01 3.990938e+00 94.33682
## Dim.6 4.199656e-01 2.210345e+00 96.54717
## Dim.7 2.354754e-01 1.239344e+00 97.78651
## Dim.8 1.835014e-01 9.657967e-01 98.75231
## Dim.9 1.114548e-01 5.866043e-01 99.33891
## Dim.10 6.889043e-02 3.625812e-01 99.70149
## Dim.11 3.523408e-02 1.854425e-01 99.88693
## Dim.12 1.378479e-02 7.255153e-02 99.95949
## Dim.13 7.014233e-03 3.691702e-02 99.99640
## Dim.14 6.742830e-04 3.548858e-03 99.99995
## Dim.15 7.732127e-06 4.069540e-05 99.99999
## Dim.16 1.479589e-06 7.787311e-06 100.00000
## Dim.17 2.494574e-31 1.312933e-30 100.00000
## Dim.18 9.583700e-33 5.044052e-32 100.00000
## Dim.19 7.740154e-33 4.073765e-32 100.00000- The proportion of variance is represented by an eigenvalue in the
second column, For example, Dim.1 has an eigenvalue of 15.393, which
corresponds to a variance percentage of 66.92852
- We can limit the number of principal components to a certain fraction of the total variance (eg > 70%).
fviz_eig(data.pca, addlabels = TRUE, ylim = c(0, 100)) +
geom_vline(xintercept = 3, linetype = "dashed", color = "salmon", size = 1)## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.
fviz_pca_ind(data.pca,
geom.ind = "point", # show points only (nbut not "text")
col.ind = data$Team.Level, # color by groups
palette = c("#00AFBB", "#E7B800", "#FC4E07"),
addEllipses = TRUE, # Concentration ellipses
legend.title = "Groups"
)
data.pca## **Results for the Principal Component Analysis (PCA)**
## The analysis was performed on 20 individuals, described by 19 variables
## *The results are available in the following objects:
##
## name description
## 1 "$eig" "eigenvalues"
## 2 "$var" "results for the variables"
## 3 "$var$coord" "coord. for the variables"
## 4 "$var$cor" "correlations variables - dimensions"
## 5 "$var$cos2" "cos2 for the variables"
## 6 "$var$contrib" "contributions of the variables"
## 7 "$ind" "results for the individuals"
## 8 "$ind$coord" "coord. for the individuals"
## 9 "$ind$cos2" "cos2 for the individuals"
## 10 "$ind$contrib" "contributions of the individuals"
## 11 "$call" "summary statistics"
## 12 "$call$centre" "mean of the variables"
## 13 "$call$ecart.type" "standard error of the variables"
## 14 "$call$row.w" "weights for the individuals"
## 15 "$call$col.w" "weights for the variables"explained_variance <- data.pca$eig[, 2]
pca_3d <- as.data.frame(data.pca$ind$coord)
pca_3d$Team.Level <- data$Team.Level
plot_ly(pca_3d, x = ~Dim.1, y = ~Dim.2, z = ~Dim.3, color = ~Team.Level, colors = c("#00AFBB", "#E7B800", "#FC4E07")) %>%
add_markers() %>%
layout(scene = list(xaxis = list(title = paste0('Dim1 (', round(explained_variance[1], 2), '%)')),
yaxis = list(title = paste0('Dim2 (', round(explained_variance[2], 2), '%)')),
zaxis = list(title = paste0('Dim3 (', round(explained_variance[3], 2), '%)'))),
title = "3D PCA Plot of La Liga Teams")loadings <- as.data.frame(data.pca$var$coord)
loadings$Variable <- rownames(loadings)
loadings## Dim.1 Dim.2 Dim.3 Dim.4
## Points 0.9610355 -0.14612550 0.14831165 0.08488793
## Wins 0.9502959 -0.12095188 0.24193789 0.04219864
## Draws -0.5456861 -0.07247303 -0.71339332 0.22742322
## Loses -0.9199389 0.20154147 0.10762572 -0.19059739
## Goals.scored 0.9347944 0.32484416 -0.02716391 -0.08463933
## Goals.conceded -0.7856982 0.53608151 -0.06893795 -0.16196976
## Difference.goals 0.9881537 -0.04676619 0.01553648 0.02293414
## Percentage.scored.goals 0.9352299 0.32401622 -0.02529418 -0.08351271
## Percentage.conceded.goals -0.7862606 0.53541203 -0.06984591 -0.16239848
## Shots 0.7853454 0.43773449 -0.18135404 0.07079497
## Shots.on.goal 0.8708401 0.39473982 -0.11076218 0.03167907
## Penalties.scored 0.5606864 0.41870702 0.10741196 -0.39974717
## Assistances 0.9358765 0.27016711 -0.03252452 -0.04133849
## Fouls.made -0.6392594 0.13758682 0.64679785 0.15528033
## Matches.without.conceding 0.7539423 -0.57383667 0.18911310 0.12899563
## Yellow.cards -0.8406716 0.18027712 0.40229603 -0.01469528
## Red.cards -0.5381657 0.53096898 0.09592143 0.55862442
## Offsides 0.5739901 0.52830822 0.06145683 0.38851630
## Effectiveness.Percentage 0.8812976 0.18431942 0.10940898 -0.05263299
## Dim.5 Variable
## Points -0.004011597 Points
## Wins -0.051608265 Wins
## Draws 0.316865928 Draws
## Loses -0.120956689 Loses
## Goals.scored -0.047228868 Goals.scored
## Goals.conceded -0.072294248 Goals.conceded
## Difference.goals 0.004076686 Difference.goals
## Percentage.scored.goals -0.045045421 Percentage.scored.goals
## Percentage.conceded.goals -0.068074579 Percentage.conceded.goals
## Shots -0.310997074 Shots
## Shots.on.goal -0.186965768 Shots.on.goal
## Penalties.scored 0.476279539 Penalties.scored
## Assistances -0.152332976 Assistances
## Fouls.made 0.180048091 Fouls.made
## Matches.without.conceding -0.040287580 Matches.without.conceding
## Yellow.cards -0.076464634 Yellow.cards
## Red.cards -0.143688399 Red.cards
## Offsides 0.396105174 Offsides
## Effectiveness.Percentage 0.165140994 Effectiveness.Percentagep1 <- ggplot(loadings, aes(x = reorder(Variable, Dim.1), y = Dim.1)) +
geom_bar(stat = "identity", fill = "skyblue") +
coord_flip() +
labs(title = "Loadings on PC1", x = "Variables", y = "Loadings") +
theme_minimal()
p2 <- ggplot(loadings, aes(x = reorder(Variable, Dim.2), y = Dim.2)) +
geom_bar(stat = "identity", fill = "salmon") +
coord_flip() +
labs(title = "Loadings on PC2", x = "Variables", y = "Loadings") +
theme_minimal()
grid.arrange(p1, p2, nrow = 2)
contrib_PC1 <- as.data.frame(data.pca$var$contrib[,1])
colnames(contrib_PC1) <- c("Contribution")
contrib_PC1$Variable <- rownames(contrib_PC1)
contrib_PC2 <- as.data.frame(data.pca$var$contrib[,2])
colnames(contrib_PC2) <- c("Contribution")
contrib_PC2$Variable <- rownames(contrib_PC2)
p1 = ggplot(contrib_PC1, aes(x = reorder(Variable, Contribution), y = Contribution)) +
geom_bar(stat = "identity", fill = "skyblue") +
coord_flip() +
labs(title = "Contribution of Variables to Dim 1", x = "", y = "Contribution (%)") +
theme_minimal()
p2 = ggplot(contrib_PC2, aes(x = reorder(Variable, Contribution), y = Contribution)) +
geom_bar(stat = "identity", fill = "skyblue") +
coord_flip() +
labs(title = "Contribution of Variables to Dim 2", x = "", y = "Contribution (%)") +
theme_minimal()
grid.arrange(p1, p2, ncol=2)
PC1 <- data.pca$ind$coord[, 1]
PC2 <- data.pca$ind$coord[, 2]pca_scores <- as.data.frame(data.pca$ind$coord)
pca_scores$Team <- data$Team
plot_list <- list()
p1 <- ggplot(pca_scores, aes(x = Team, y = Dim.1)) +
geom_bar(stat = "identity", fill = "skyblue") +
labs(title = "Scores on PC1 for Each Team", x = "Team", y = "Score on PC1") +
theme(axis.text.x = element_text(angle = 90, hjust = 1))
p2 <- ggplot(pca_scores, aes(x = Team, y = Dim.2)) +
geom_bar(stat = "identity", fill = "salmon") +
labs(title = "Scores on PC2 for Each Team", x = "Team", y = "Score on PC2") +
theme(axis.text.x = element_text(angle = 90, hjust = 1))
grid.arrange(p1, p2, ncol = 2)
- Analyzing the scores on the first principal component (PC1) of the
La Liga teams helps us understand the main distinctions between the
teams based on the input variables used in the PCA.
- Teams with high scores on PC1: Athletic, Atletico
Madrid, Barcelona, Real Marid: These teams may have very different
characteristics and performance that stand out from the other teams in
the original data. They may have better records,more assistances ,more
wins,more successful passes and make more dynamic attacking
transitions.
- Teams with low scores on PC1: Espanyol, Getafe,
Granada, Levante, Sporting Gijon: These teams have significantly
negative scores on PC1. This suggests that they may have the opposite
characteristics to high scoring teams. They may have poorer performance,
poorer records, or lower performance metrics and tend to commit more
fouls.
- Teams with negative scores but not too low on PC1:
They may have below average performance, they may struggle in
competition, but they are not the worst teams.
- Teams with high scores on PC1: Athletic, Atletico
Madrid, Barcelona, Real Marid: These teams may have very different
characteristics and performance that stand out from the other teams in
the original data. They may have better records,more assistances ,more
wins,more successful passes and make more dynamic attacking
transitions.
- While PC1 explains the overall performance of teams, PC2 focuses on
variables that reflect the team’s defensive performance, including the
number of matches without conceding a goal, the number of goals
conceded, the ratio of goals conceded to total goals conceded, the
number of red cards, and the number of offsides.
Teams with high scores on PC2: Rayo Vallecano, Real Madrid, Granada,..: Teams with high PC2 scores typically exhibit strong defensive records, characterized by numerous clean sheets and a tendency to concede relatively few goals. Their disciplined approach is evident in the lower incidence of red cards, reflecting a commitment to maintaining defensive stability. Moreover, these teams often adopt a tactically aggressive style of play, resulting in a higher number of offsides for the opposition. This proactive defensive approach helps in disrupting opponent attacks and controlling the flow of the game.
Teams with low scores on PC2: Teams with low PC2 scores typically demonstrate weaker defensive records, characterized by fewer clean sheets and a tendency to concede more goals. Their poor discipline is evident in higher red card counts, indicating a lack of control and organization on the defensive end. Additionally, these teams often employ less aggressive tactics, leading to fewer offsides for the opposition. This defensive approach may lack proactive measures to disrupt opponent attacks effectively, resulting in a higher vulnerability to conceding goals.
Specific to Atlético Madrid: Reason for Low PC2 Score: Despite many clean sheets, other factors such as a higher number of fouls and red cards negatively impact their PC2 score. Their aggressive defensive style might result in fewer offsides, contributing to a lower score.
3. Discussion
- In this analysis, we have explored the Olympic dataset and performed a Principal Components Analysis (PCA) to identify the underlying structure of the data. We found that the first three principal components explain 80.3% of the total variance, which is a good starting point for further analysis. We visualized the data in a 3D plot and identified the main variables that contribute to each principal component. We also visualized the scores of each nation on the first two principal components. This analysis provides valuable insights into the performance of different nations in the Olympic games and can help identify patterns and trends in the data.
- The results showed that the best teams were characterized and differentiated from the bottom teams by completing more successful passes and making more dynamic attacking transitions. The bottom teams were characterized by making more defensive than attacking moves, scoring fewer goals and spending more time in the final third of the pitch.